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math.LO2026
Axiomatic Justification in Constructive Morse Set Theory
Douglas S. Bridges
Working within Constructive Morse Set Theory (CMST), we introduce axioms for a new notion, jst Pp, intended to capture what it means for P to prove, or justify, p under the BHK int…
math.LO2026
Monotone convergence theorems equivalent to Markov's principle
Douglas S. Bridges
The notions of provisional, negative, and apparent convergence to 0 are introduced. It is then shown that Markov's principle is equivalent, in Bishop-style constructive mathematics…
math.LO2026
On Constructive Connectedness Properties
Douglas S. Bridges
We plug two gaps in the constructive proof of Theorem 1 (respectively, Theorem 2) in <cite>dsb</cite>, showing that the property of C-connectedness (respectively, O-connectedness)…